Not Applicable
Not Applicable
The present invention relates to an educational aid used in teaching and learning basic mathematics.
Prior art known to Applicant discloses that there has been many inventions of appliances, devices, apparatuses, aids . . . which have been used to help teach and learn basic mathematics. Following are some of most related inventions which may be of interest regarding the present invention:
xe2x80x9cEducational Appliancexe2x80x9d, U.S. Pat. No. 1,163,125 to A. Bechmann in Dec. 7, 1915.
xe2x80x9cEducational Devicexe2x80x9d, U.S. Pat. No. 1,400,887 to H. Liebman in Dec. 20, 1921.
xe2x80x9cMethod of Teaching Mathematicsxe2x80x9d, U.S. Pat. No. 4,445,865 to J. Sellon in May 1, 1984.
xe2x80x9cMathematics Teaching Devicexe2x80x9d, U.S. Pat. No. 5,759,041 to B. Batten in Jun. 2, 1998.
xe2x80x9cFlexible Planar Apparatusxe2x80x9d, U.S. Pat. No. 5,997,305 to L. Mangles in Dec. 7, 1999.
All of above inventions present something similar to times table with indicators (sticks, pins, colored transparent strips, or tip of a pencil . . . ) or hand folding (U.S. Pat. No. 5,997,305 ) used to locate product for two given factors. Some of inventions above are also used to teach addition, subtraction and division.
While times table and similar devices have been known and used for a long time, and partially accomplished some of objects and advantages in teaching and learning basic mathematics, they present a number of drawbacks. First, times table and similar devices require users to know concepts of horizontal, vertical and intersection or/and use indicators (sticks, pins, colored transparent strips . . . ) in order to find product of two factors. This requirement obviously makes it harder for the users to learn basic mathematics, especially for the young ones, for they have to learn many new things at the same time. Moreover, horizontal, vertical and intersection are concepts in higher level of mathematics, so it is not suitable to use them in teaching basic mathematics. Second, times table and similar devices show the users how to memorize but do not promote how to basically understand numbers, mathematical operations and relationship among them. For example, the users memorize that product of two factors 3 and 2 is 6 just because number 6 locates at intersection of xe2x80x9c3xe2x80x9d row and xe2x80x9c2xe2x80x9d row. Third, times table and similar devices have been primarily used to teach multiplication, maybe division also. Thus, they are proved not to be effective in teaching and learning other areas of basic mathematics. Presented are just some of the drawbacks of times table and similar devices.
Accordingly, it is seen that there exists a need to have a new educational aid which will overcome the drawbacks of the times table and similar devices, and be efficient in teaching and learning fundamental areas of basic mathematics.
The present invention is based on base-ten number system with power of ten xe2x80x9c10axe2x80x9d where xe2x80x9caxe2x80x9d is an integer with range from minus infinitive to plus infinitive.
Powers of ten locate in a plane in such a way that they form an array with powers of ten consecutively ranging from minus infinitive to plus infinitive in directions from right to left on horizontal rows, and from bottom to top on vertical rows. Preferred embodiment of the present invention is based on said plane and framed by 6xc3x976 array of powers of ten:   "AutoLeftMatch"                              10          6                                      10          5                                      10          4                                      10          3                                      10          2                                      10          1                                              10          5                                      10          4                                      10          3                                      10          2                                      10          1                                      10          0                                              10          4                                      10          3                                      10          2                                      10          1                                      10          0                                      10                      -            1                                                        10          3                                      10          2                                      10          1                                      10          0                                      10                      -            1                                                10                      -            2                                                        10          2                                      10          1                                      10          0                                      10                      -            1                                                10                      -            2                                                10                      -            3                                                        10          1                                      10          0                                      10                      -            1                                                10                      -            2                                                10                      -            3                                                10                      -            4                              
Powers of ten in the above array are then expanded, regrouped and placed in arrays of square spaces which are separated from one another with same distance. Nine arrays with rows and columns of square spaces are arranged as below, and referred as bottom right, bottom, bottom left, right, center, left, top right, top and top left arrays, in order from right to left and from bottom to top, respectively:   "AutoLeftMatch"                              (                      2            xc3x97            2                    )                                      (                      2            xc3x97            10                    )                                      (                      2            xc3x97            2                    )                                              (                      10            xc3x97            2                    )                                      (                      10            xc3x97            10                    )                                      (                      10            xc3x97            2                    )                                              (                      2            xc3x97            2                    )                                      (                      2            xc3x97            10                    )                                      (                      2            xc3x97            2                    )                    
Formation, presentation and relations of numbers or numbers, dots and dashes inside and among square spaces of the arrays as well as with numbers, mathematical symbols, arrows, percentages, sign, equations and condition in open spaces among said arrays are used in teaching and learning fundamental areas of basic mathematics which mainly includes numbers in base-ten number system (1, 2, 3, . . . ), addition, subtraction, multiplication, division, relations of a number with zero (number 0) in mathematical operations, whole numbers, fractions, and percentage.
Following are advantages of the present invention regarding to disadvantages of the related inventions identified in section xe2x80x98Background Of The Inventionxe2x80x99:
In stead of using indicators (sticks, pins, . . . ), hand folding or/and concepts of vertical, horizontal and intersection to locate product of two factors, as with times table or similar devices, lines of same small numbers in center array of the preferred embodiment place small numbers, used as factors, next on the right and on the bottom of big number, used as product, in each square space. Product of two factors is not just accepted and memorized but it can be reasoned and proved. For example, big number 6 and 2 small numbers 2 and 3 on its right and on its bottom in same square space can be used in 6=2xc3x973 (2 and 3 as factors) or 6=2+2+2 (2 as addend with notice that 2 is added 3 times to make 6) or 6=3+3 (3 as addend with notice that 3 is added 2 times to make 6). Also, 6=4+2 and 6xe2x88x928=2 are resulted from subtraction of big numbers 4 and 8 with small number 2""s in right and left square spaces of same row. Number 6 is also resulted from subtraction and addition of numbers in top and bottom square spaces of same column. Times of number 2 in [6=2+2+2] and times of number 3 in [6=3+3] can also be used to present 6/3=2 and 6/2=3.
Thus, big number 6 with two small numbers 2 and 3 in same square space are not just used to be accepted and memorized only as xe2x80x9c6 is product of 2 and 3xe2x80x9d, but are partially used to promote a basic understanding of relationship among numbers 6, 2, 3, 4, 8 . . . , especially 6, 2, 3, and among operations 3xc3x972=6, 2+2+2=6, 3+3=6, 4+2=6, 8xe2x88x922=6, 6/3=2 and 6/2=3. Advantages of the present invention regarding to disadvantages of identified related inventions are obvious, and in these respects, the present invention substantially departs from the conventional concepts, designs, and methods of use of the prior art, to provide a new educational aid used in teaching and learning fundamental areas of basic mathematics.
Accordingly, besides objects and advantages described above, several objects and advantages of the present invention are:
(a) to provide a new educational aid;
(b) to provide a new educational aid which can be used in teaching and learning fundamental areas of basic mathematics;
(c) to provide a basic mathematics teaching and learning aid which can be used to promote minimum requiring of necessary means for teaching and basic mathematical knowledge for learning fundamental areas of basic mathematics;
(d) to provide a basic mathematics teaching and learning aid which can be used to promote basic understanding of relationship among numbers in base-ten number system as well as among basic mathematical operations;
(e) to provide a basic mathematics teaching and learning aid which can be used to promote basic understanding of meanings of basic mathematics operations;
(f) to provide a basic mathematics teaching and learning aid which can be used to promote basic preparation for teaching and learning mathematics at a higher level than basic mathematics.
(g) to provide a basic mathematics teaching and learning aid which can be manufactured with ease, readily available material, low cost and convenience for packaging and transporting;
Other objects and advantages of the present inventions are to provide a basic mathematics teaching and learning aid which is simple, compact, portable, reliable, inexpensive to the buying public, and can be used to promote wide popularizing of basic mathematics mass education.
Further objects and advantages of the present inventions will become apparent from a consideration of the accompanying drawings and following description.